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| 22 | <title>Handling NaN (GNU C Language Manual)</title>
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| 32 | <link href="Floating-Point-in-Depth.html" rel="up" title="Floating Point in Depth">
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| 55 | </head>
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| 56 |
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| 57 | <body lang="en">
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| 58 | <span id="Handling-NaN"></span><div class="header">
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| 59 | <p>
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| 60 | Next: <a href="Signed-Zeros.html" accesskey="n" rel="next">Signed Zeros</a>, Previous: <a href="Handling-Infinity.html" accesskey="p" rel="prev">Handling Infinity</a>, Up: <a href="Floating-Point-in-Depth.html" accesskey="u" rel="up">Floating Point in Depth</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Symbol-Index.html" title="Index" rel="index">Index</a>]</p>
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| 61 | </div>
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| 62 | <hr>
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| 63 | <span id="Handling-NaN-1"></span><h3 class="section">28.14 Handling NaN</h3>
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| 64 | <span id="index-NaN-in-floating_002dpoint-arithmetic"></span>
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| 65 | <span id="index-not-a-number"></span>
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| 66 | <span id="index-floating_002dpoint-NaN"></span>
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| 67 |
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| 68 | <p>NaNs are not numbers: they represent values from computations that
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| 69 | produce undefined results. They have a distinctive property that
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| 70 | makes them unlike any other floating-point value: they are
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| 71 | <em>unequal to everything, including themselves</em>! Thus, you can
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| 72 | write a test for a NaN like this:
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| 73 | </p>
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| 74 | <div class="example">
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| 75 | <pre class="example">if (x != x)
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| 76 | printf ("x is a NaN\n");
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| 77 | </pre></div>
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| 78 |
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| 79 | <p>This test works in GNU C, but some compilers might evaluate that test
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| 80 | expression as false without properly checking for the NaN value.
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| 81 | A more portable way to test for NaN is to use the <code>isnan</code>
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| 82 | function declared in <code>math.h</code>:
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| 83 | </p>
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| 84 | <div class="example">
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| 85 | <pre class="example">if (isnan (x))
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| 86 | printf ("x is a NaN\n");
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| 87 | </pre></div>
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| 88 |
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| 89 | <p>See <a href="https://www.gnu.org/software/libc/manual/html_node/Floating-Point-Classes.html#Floating-Point-Classes">Floating Point Classes</a> in <cite>The GNU C Library Reference Manual</cite>.
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| 90 | </p>
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| 91 | <p>One important use of NaNs is marking of missing data. For
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| 92 | example, in statistics, such data must be omitted from
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| 93 | computations. Use of any particular finite value for missing
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| 94 | data would eventually collide with real data, whereas such data
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| 95 | could never be a NaN, so it is an ideal marker. Functions that
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| 96 | deal with collections of data that may have holes can be written
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| 97 | to test for, and ignore, NaN values.
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| 98 | </p>
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| 99 | <p>It is easy to generate a NaN in computations: evaluating <code>0.0 /
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| 100 | 0.0</code> is the commonest way, but <code>Infinity - Infinity</code>,
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| 101 | <code>Infinity / Infinity</code>, and <code>sqrt (-1.0)</code> also work.
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| 102 | Functions that receive out-of-bounds arguments can choose to return a
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| 103 | stored NaN value, such as with the <code>NAN</code> macro defined in
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| 104 | <code>math.h</code>, but that does not set the <em>invalid operand</em>
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| 105 | exception flag, and that can fool some programs.
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| 106 | </p>
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| 107 | <span id="index-NaNs_002dalways_002dpropagate-rule"></span>
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| 108 | <p>Like Infinity, NaNs propagate in computations, but they are even
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| 109 | stickier, because they never disappear in division. Thus, once a
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| 110 | NaN appears in a chain of numerical operations, it is almost
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| 111 | certain to pop out into the final results. The programmer
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| 112 | has to decide whether that is expected, or whether there is a
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| 113 | coding or algorithmic error that needs repair.
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| 114 | </p>
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| 115 | <p>In general, when function gets a NaN argument, it usually returns a
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| 116 | NaN. However, there are some exceptions in the math-library functions
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| 117 | that you need to be aware of, because they violate the
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| 118 | <em>NaNs-always-propagate</em> rule:
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| 119 | </p>
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| 120 | <ul>
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| 121 | <li> <code>pow (x, 0.0)</code> always returns <code>1.0</code>, even if <code>x</code> is
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| 122 | 0.0, Infinity, or a NaN.
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| 123 |
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| 124 | </li><li> <code>pow (1, y)</code> always returns <code>1</code>, even if <code>y</code> is a NaN.
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| 125 |
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| 126 | </li><li> <code>hypot (INFINITY, y)</code> and <code>hypot (-INFINITY, y)</code> both
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| 127 | always return <code>INFINITY</code>, even if <code>y</code> is a Nan.
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| 128 |
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| 129 | </li><li> If just one of the arguments to <code>fmax (x, y)</code> or
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| 130 | <code>fmin (x, y)</code> is a NaN, it returns the other argument. If
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| 131 | both arguments are NaNs, it returns a NaN, but there is no
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| 132 | requirement about where it comes from: it could be <code>x</code>, or
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| 133 | <code>y</code>, or some other quiet NaN.
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| 134 | </li></ul>
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| 135 |
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| 136 | <p>NaNs are also used for the return values of math-library
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| 137 | functions where the result is not representable in real
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| 138 | arithmetic, or is mathematically undefined or uncertain, such as
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| 139 | <code>sqrt (-1.0)</code> and <code>sin (Infinity)</code>. However, note that a
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| 140 | result that is merely too big to represent should always produce
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| 141 | an Infinity, such as with <code>exp (1000.0)</code> (too big) and
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| 142 | <code>exp (Infinity)</code> (truly infinite).
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| 143 | </p>
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| 144 |
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| 145 | <hr>
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| 146 | <div class="header">
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| 147 | <p>
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| 148 | Next: <a href="Signed-Zeros.html" accesskey="n" rel="next">Signed Zeros</a>, Previous: <a href="Handling-Infinity.html" accesskey="p" rel="prev">Handling Infinity</a>, Up: <a href="Floating-Point-in-Depth.html" accesskey="u" rel="up">Floating Point in Depth</a> [<a href="index.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="Symbol-Index.html" title="Index" rel="index">Index</a>]</p>
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